D. Cherkashin

collaborators

8 papers

math.CO2026

On uniform eventowns

Danila Cherkashin, Pavel Prozorov

Suppose that $n = 2 m$ , $k = 2 t$ and $n > 10 k^{7}$ . We show that if a family $F$ of $k$ -subsets of an $n$ -set has only even pairwise intersections then $|\mathcal F| \leq \binom…

math.CO2026

Short proofs of three combinatorial results in the Johnson scheme

Danila Cherkashin, Yakov Shubin

In this note, we give short proofs of three theorems concerning extremal problems in the Johnson scheme, or, in other terminology, on $(n, k, L)$ -systems. The main result is a proof…

math.MG2026

Universal Ahlfors--David regularity of Steiner trees

Danila Cherkashin, Pavel Prozorov, Yana Teplitskaya

The celebrated Steiner tree problem is the problem of finding a set $S t$ of minimum one-dimensional Hausdorff measure $H$ (length) such that $S t \cup A$ is connected, whe…

math.CO2025

On the chromatic numbers of Johnson type graphs

Danila Cherkashin

A Johnson type graph $J_{\pm} (n, k, t)$ is a graph whose vertex set consists of vectors from ${- 1, 0, 1}^{n}$ of the length $k$ and edges connect vertices with scalar product $t…

math.MG2025

On branching points in the Gilbert-Steiner problem

Danila Cherkashin

The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transp…

math.CO2025

The number of trees in distance-hereditary graphs and their friends

Danila Cherkashin, Pavel Prozorov

Counting the number of spanning trees in specific classes of graphs has attracted increasing attention in recent years. In this note, we present unified proofs and generalizations…